Question

Suppose S is a set containing 5 elements, and that ⪯ is a total ordering of S. Draw the Hasse diagram for ⪯ (no need to label the vertices in your diagram).

Answer 1

A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point is drawn for each element of the poset, and line segments are drawn between these points according to the following two rules:

1. If $x<y$  in the poset, then the point corresponding to $x$  appears lower in the drawing than the point corresponding to $y$ .

2. The line segment between the points corresponding to any two elements $x$ and y  of the poset is included in the drawing iff $x$  covers y or $y$  covers $x$.